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{{r|Holomorphic function}}

...rm '''''[[analytic function]]''''' is often used interchangeably with '''''holomorphic function''''', although the term '''''[[analytic function|analytic]]''''' is also us ...This is also because an important result in complex analysis is that every holomorphic function is complex analytic, a fact that does not follow directly from the definiti

*is [[holomorphic function|holomorphic]] at a point ''a'' [[iff]] it is differentiable at every point

{{r|Holomorphic function}}

...en mapping theorem for complex functions''. Let ''f'' be a non-constant [[holomorphic function]] on an open domain ''D'' in the [[complex plane]]. Then ''f'' is an open

{{r|Holomorphic function}}

{{r|Holomorphic function}}

{{r|holomorphic function}}

{{r|Holomorphic function}}

...ration. This approximation is especially recommended if the integrand is [[holomorphic function|holomorphic]] in a neighbourhood of integration interval. If the integrand is a [[holomorphic function]] along the path of integration, then the error of approximation decreases

'''ArcSin''', or '''asign''', or '''arcsin''' is [[holomorphic function]], inverse of [[sine|sin]].

an '''entire function''' is a [[function (mathematics)|function]] that is [[holomorphic function|holomorphic]] in the whole [[complex plane]]

{{r|Holomorphic function}}

{{r|Holomorphic function}}

{{r|Holomorphic function}}

For the non–integer iterates, it should be assumed that <math>T</math> is [[holomorphic function]], and the superfunction <math>G</math> is also expected to be holomorphic. ...x) iterate of the transfer function <math>T</math> is straightforward; any holomorphic function can be declared as a [[transfer function]] and iterated any number of times

For a [[holomorphic function]], the contour lines for the real part are orthogonal to those for the imag

...x variable then both <math> p(z)</math> and <math> 1/p(z)</math> will be [[holomorphic function|holomorphic]] in any domain where <math>\scriptstyle p(z) \ne 0</math>. But

the Taylor series can be used to make the [[polynomial approximation]] of [[holomorphic function]]s, just truncating the series.

...more lucky than the <math>~\sqrt{!~}~~</math>; at least the existence of [[holomorphic function]] superfunction (from <math>a</math> to <math>b</math>) of [[holomorphic function]] <math>~f~</math> on domain <math>D</math> is